A Novel Generator of Continuous Probability Distributions for the Asymmetric Left-skewed Bimodal Real-life Data with Properties and Copulas

Abstract

This paper presents a novel two-parameter G family of distributions. Relevant statistical properties such as the ordinary moments, incomplete moments and moment generating function are derived. Using common copulas, some new bivariate type G families are derived. Special attention is devoted to the standard exponential base line model. The density of the new exponential extension can be “asymmetric and right skewed shape” with no peak, “asymmetric right skewed shape” with one peak, “symmetric shape” and “asymmetric left skewed shape” with one peak. The hazard rate of the new exponential distribution can be “increasing”, “U-shape”, “decreasing” and “J-shape”. The usefulness and flexibility of the new family is illustrated by means of two applications to real data sets. The new family is compared with many common G families in modeling relief times and survival times data sets.

Modified Bagdonavicius-Nikulin Goodness-of-fit Test Statistic for the Compound Topp Leone Burr XII Model with Various Censored Applications

“…• The CDF in (2) can be used for presenting a new discrete probability distribution for modeling the count data (see Aboraya et al [1], Ibrahim et al [30], Chesneau et al [17] and Yousof et al [60] for more details). • Many future works may be allocated to study these new bivariate Poisson Topp-Leone Burr XII distributions under some copulas (see Shehata and Yousof [50], Shehata and Yousof [51], Al-babtain et al [6], Shehata et al [53], Elgohari and Yousof [20], Elgohari and Yousof [21], Elgohari and Yousof [22], Elgohari et al [23] and Shehata et al [52]). • Some new acceptance sampling plans based on the Poisson Topp-Leone Burr XII distribution can be presented in separate article (see Ahmed and Yousof [4] and Ahmed et al [5]).…”

Transmuted Ailamujia Distribution with Applications to Lifetime Observations

“…The first dataset represents the relief time (in minutes) of patients receiving analgesic. The data was first reported in [17] and also appeared in several propositions [16], [18][19][20] involving lifetime distributions. The second dataset consists of the running times and times of failures of sampled devices from a tracking study of a large system as reported in [21].…”

Asymmetric Density for Risk Claim-Size Data: Prediction and Bimodal Data Applications

“…It is worth mentioning that this insurance-claims data are first analyzed under a probability-based distribution. However, many other interesting insurance data can be analyzed using the new model; see, for example, [19] (for extreme value theory as a risk management tool with useful applications), [20] (for a review in skewed distributions in finance and actuarial science), [21] (for details about modeling claims data with composite Stoppa models), [22] (for more right censored medical and reliability data sets), [23] (for the jointly modeling area-level crash rates by severity with Bayesian multivariate random-parameters spatiotemporal Tobit regression), [24] (for the investigating the impacts of real-time weather conditions on freeway crash severity), [25] (for more copulas and a modified right censored test for validation) and [26] (for an alternative four-parameter exponentiated Weibull model with Copula, properties and real data modeling). For modeling the claims data, we first need to explore it.…”